Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is 2i – 3j + 6k. [Delhi 2016]

Show that the vectors a, b, and c are co-planar if a + b + c and c + a are co-planar. [Delhi 2016]

Find the coordinate of the point P where the line through A(3, – 4, –5) and B (2, –3, 1) crosses the plane passing through three points L(2, 2, 1), M(3, 0, 1) and N(4, –1, 0). Also, find the ratio in which P divides the line segment AB. [Delhi 2016]

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0. Then find the distance of plane thus obtained from the point A(1, 3, 6). [Delhi 2015C]